The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 1.6% per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2017. Round your answer to 1 decimal place.
Answers
The form of an exponential growth model is:
\(y=y_0e^{rt}\)Where:
• y0 is the initial population
,• r is the rate of annual growth, in decimal
,• t are years since 1987
In this case:
y0 is 5 billion.
The annual growth rate is 1.6%. To covert to decimal, we divide by 100:
\(\frac{1.6}{100}=0.016\)r = 0.016
And t are the years since 1987. We want to find the population in 2017. Then:
\(t=2017-1987=30\)We can construct the model equation:
\(y=5,000,000,000e^{0.016\cdot30}\)
And solve:
\(y=8,080,372,011\)This is the projected world population in 2017
Related Questions
Last year, the Ross family spent $3,336 for electricity. They are opting to use balanced billing for next year. What will their monthly payment be?
Answers
Using balanced billing, the monthly payment is $278
What will be their monthly payment?Using balanced billing to determine their monthly payment, we simply need to divide their total annual payment by the total number of months in a year. This will result to dividing the entire annual bill by 12 to determine the monthly payment.
Given that the Ross family spent $3,336 for electricity last year, we can calculate their monthly payment as follows:
Monthly payment = Total cost / Number of months
Monthly payment = $3,336 / 12
Monthly payment = $278
Therefore, the Ross family's monthly payment for balanced billing will be approximately $278.
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. A box contains 10 balls, numbered 1 through 10 (so the balls are distinct). a. A ball is drawn from the box at random. Compute the probability that the number on the ball was 3, 4, or 5. b. A ball is chosen at random and then a second ball is chosen at random from the remaining nine balls. Find the probability that the numbers on the two selected balls differ by 2 or more. c. Three balls are chosen (with replacement). Find the probability that the sum of the numbers on the balls is even.
Answers
Answer:
A) 0.30
B) 0.9
C) 0.4
Step-by-step explanation:
Number of balls = 10
A ) probability that a ball drawn at random is numbered 3,4 or 5
number on ball to be drawn = 3 i.e 3,4 or 5
total number of balls = 10
hence the probability = 3 / 10 = 0.30
B ) probability that number written on two different balls drawn at random differs by 2 or more
p( numbers differ by 1 ) = 9 * (1/10) * (1/9) = 0.1
p( numbers on two balls differ by 2 or more ) = 1 - p( numbers differ by 1 )
= 1 - 0.1 = 0.9
C ) Probabilty that the sum of the numbers on 3 balls chosen is even
even numbers = 5 which are ( 2,4,6,8,10 )
The even numbers that can be gotten by summation of three balls are
(4.6,8,10 ) = 4
hence the probability of picking three balls with replacement whose sum = even number will be
= 4 / 10 = 0.4
OMG PLS HELP ME!!!! 30 pts!!!!! I NEED DIS ASAP
A large downtown hotel consists of twenty-four levels. Any level above ground is referred to as a" floor". There are twenty-two floors and each floor corresponds to its number on the number line (2 is second floor, 3 is third floor, etc...) and two underground levels reserved for underground parking. The first level below ground level is Parking A, and the second level below ground level is labeled Parking B.
If you start at Parking B and take the elevator to the fourteenth floor, how many levels have you gone up? [Type your answer as a number.]
Answers
Answer:
16
Step-by-step explanation:
there is 2 underground and 14 above so 2 + 14 = 16
Find the standard form of the equation of the line through (8,-3) that is parallel to the line 3y=4x+8
Answers
The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41
How to represent equation in standard form?The equation of the line in standard form can be represented as follows:
Ax + By = C
where
A, B and C are constantTherefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;
Parallel lines have the same slope.
Hence,
3y = 4x + 8
y = 4 / 3 x + 8 / 3
The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.
y = 4 / 3 x + b
-3 = 4 / 3 (8) + b
b = -3 - 32 / 3
b = -9 - 32/ 3
b = -41 / 3
Hence,
y = 4 / 3 x - 41 / 3
multiply through by 3
3y = 4x - 41
Therefore, the standard form is 4x - 3y = 41
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Last year, the debate club had 16 members. This year, the club has 10 members. What is the percent of change in the number of club members?
Answers
Answer:
-60%
Step-by-step explanation:
The formula for percent change is [ x2-x1/x1 ].
10-16/10
-6/10 or -0.6
~Multiply by 100%
-0.6 * 100% = -60%
Best of Luck!
A sample of a radioactive substance has an initial mass of 58.7 . This substance follows a continuous exponential decay model and has a half-life of 5 hours. (a)Let t be the time (in hours) since the start of the experiment, and let y be the amount of the substance at time t . Write a formula relating y to t. y=__ e^__(t) . Use exact expressions to fill in the missing parts of the formula. Do not use approximations. b)How much will be present in 8 hours? Do not round any intermediate computations, and round your answer to the nearest tenth.
Answers
Answer:
a). Y = y0e^-k(t)
b) Y = 19.4 Unit mass
Step-by-step explanation:
Y = y0e^-k(t)
Where y is amount present at the time
Y0 is initial amount present at t = 0
Y0 = 58.7
Half life = 5 hours
At half life , y = 58.7/2
At half life , y = 29.35
K = decaying constant.
Let's look fithe value of k
Y = y0e^-k(t)
29.35 = 58.7e^-k(5)
29.35/58.7 = e^-k(5)
0.5 = e^-k(5)
In 0.5 = -k(5)
-0.69314718 = -k(5)
0.138629436 = k
The value present in 8 hours will be
Y = y0e^-k(t)
Y = 58.7e-0.138629436(8)
Y = 58.7e-1.109035488
Y = 58.7(0.329876978)
Y= 19.36377861
To the nearest tenth
Y = 19.4 unit of mass
Mr. Smith and Mr. Stein were driving to a business meeting 140 miles from their office. Mr. Smith drove the first
miles, then Mr. Stein drove the rest of the way.
Write an algebraic expression for how many miles Mr. Stein drove
Answers
This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.
How to determine the algebraic expression?An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can be simplified, evaluated, or manipulated using algebraic rules and properties.
Let x be the number of miles Mr. Smith drove. Then, the number of miles Mr. Stein drove is \(140 - x\) , since they drove a total of 140 miles and Mr. Smith already drove x miles.
the algebraic expression for how many miles Mr. Stein drove is:
\(140 - x\)
Therefore, This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.
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How much space will a cylindrical water tank occupy if its height is 100 cm and its diameter is 30
find the volume
Answers
Answer:
volume of a cylindrical water tank = 70,650cm³
Step-by-step explanation:
volume of cylinder, V = πr²h
where π = 3.14
h = 100cm
r = ?
given is diameter = 30cm
r = d/2 = 30/2 = 15cm
substituting the values in the formula,
V = 3.14 * 15² * 100
= 3.14 * 225 * 100
= 70,650cm³
Answer:
How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm
Volume: 706,500 cm³
Step-by-step explanation:
How much space it would take up:
To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.
The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.
To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.
A = π(15 cm)²
A = π(225 cm²)
A ≈ 706.86 cm²
So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.
The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.
Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.
Volume:
To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
First, we need to find the radius by dividing the diameter by 2:
Radius = 30 cm / 2 = 15 cm
Now we can calculate the volume:
V = π(15 cm)²(100 cm)
V = 3.14 * 225 cm² * 100 cm
V = 706,500 cm³
Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.
PLEASE ANSWER PO I NEED IT RN AND PLEASE BE SERIOUS IN ANSWERING
A dump truck is loaded with 2.595 cubic meter of sand. How many cubic decimeters of sand are loaded on the truck?
Answers
2595 cubic decimeters
1 cubic meter = 1000 cubic decimeters
so 2.595 cubic meter = (2.595 × 1000) cubic decimeters
= 2595 cubic decimeters
A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 26 ft long and 20 ft wide.
Find the area of the garden. Use the value 3.14 for it, and do not round your answer.
Answers
Answer:
26 multiplied by 20 is 529 which is the area
Step-by-step explanation: hi
The hypothesis that motivates most studies and is usually the reason the data are being collected in the first place is the __________ hypothesis.Group of answer choicesnullalternativenormativetestalgorithmic
Answers
The hypothesis which motivates the studies which is usually the reason for any data is being collected at first place is called alternative hypothesis.
A hypothesis is an exact clarification that pertains to the set of data that may be examined with the aid of using positive similarly investigations. There are essentially types, namely, null speculation and opportunity speculation. A studies commonly begins offevolved with a hassle. Next, those hypotheses offer the researcher with a few precise restatements and clarifications of the studies hassle.
The standards of the studies hassle withinside the shape of null hypothesis and opportunity hypothesis need to be expressed as a dating among or extra variables. The standards is that the statements need to be the only that expresses the connection among the 2 or extra measurable variables. The null hypothesis and opportunity speculation need to bring clean implications for checking out and mentioning relations.
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Correct Question:
The hypothesis that motivates most studies and is usually the reason the data are being collected in the first place is the __________ hypothesis.
the density of the copper is 9.86g/cm\(x^{3}\)
![the density of the copper is 9.86g/cm[tex]x^{3}[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/kBdJoEKedYKgyZmbWgXrufRB5h52H33f.png)
Answers
The mass of the cubic cuboid is 1.479 kilograms.
What is the mass of a copper cuboid?
Dimensionally speaking, density (ρ), in kilograms per cubic meter, is mass (m), in kilograms, per unit volume (V), in cubic meters. By the assumption of uniform density within the copper cuboid, the mass of the solid is equal to:
m = ρ · V
Where V is the volume of cuboid, in cubic meters.
And the volume of cuboid is:
V = w · h · l
Where:
w - Width, in meters. h - Height, in meters.l - Length, in meters.Please notice that a kilogram equals 1000 grams and a meter equals 100 centimeters.
First, calculate the volume of the cuboid:
V = (0.05 m) · (0.03 m) · (0.10 m)
V = 1.5 × 10⁻⁴ m³
Second, determine the mass of the cuboid:
m = (9.86 g / cm³) · (1 kg / 1000 g) · (1000000 cm³ / m³) · (1.5 × 10⁻⁴ m³)
m = 1.479 kg
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This table shows the cost of renting a kayak.
Hours Cost
1. $13
2. $21
3. $29
4. $37
5. $45
The cost of renting a kayak is represented by the equation
y = 8x + 5, where x represents the number of hours. What
does the slope of the equation represent?
Answers
9514 1404 393
Answer:
dollars per hour
Step-by-step explanation:
If m is the slope, the units of m can be found by considering the units of x and y.
y is in dollars
x is in hours
Then from the point of view of units, we have ...
dollars = m × hours
m = dollars/hours
The slope in the equation is the rental charge in dollars per hour.
Astronomers believe that the radius of a variable star increases and decreases with the brightness of the star. Suppose a variable star has an average radius of 20 million miles and changes by a maximum of 1.6 million miles from this average during a single pulsation, and that the time between periods of maximum brightness is 5.2 days. Find an equation that describes the radius of this star as a function of time. (Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing.) R(t) =
Answers
Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then R(t) = 20 + 1.6sin(2πt/5.2).
The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.
In this case, the amplitude is 1.6.
Since the radius changes by a maximum of 1.6 million miles.
The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)
The phase shift is 0, since when t = 0 the radius is increasing.
The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)
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Joan received $100 in gift cards for an online music store. Each time she buys a new song it costs $1.29. She has already bought 10 songs. Write an inequality that models this situation. Then determine the number of songs she can buy and not run out of gift card money
Answers
The inequality of context is 1.29x + 10(1.29) ≤ 100 and she can buy 77 songs.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Let, The number of new songs be 'x'.
Therefore, The inequality to determine the number of songs she can buy and not run out of gift card money is,
1.29x + 10(1.29) ≤ 100.
1.29x + 12.9 ≤ 100.
1.29x ≤ 87.1.
x ≤ 87.1/1.29.
x ≤ 67.52 But she can buy only 67 songs and 10 songs before so 77 songs.
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Please help theres two questions (-2x+8y-11)+(-3y-y+5)
(A) what are the like terms in the two Linear expressions
(B) what is the sum of the linear expressions? Express your answer in simplist form. SHOW YOUR WORK. 100 POINTS
(-2x+8y-11)+(-3y-y+5)
Answers
Answer:
a) "Like terms" are terms whose variables (and their exponents such as the 2 in x²) are the same
8y, -3y and y are all likes terms because the variables are all y
b)
\((-2x+8y-11)+(-3y-y+5)\\\\=-2x+8y-11-3y-y+5\\\\=-2x+(8y-3y-y)+(5-11)\\\\=-2x+4y-6\\\\=2(-x+2y-3)\\\\=-2(x-2y+3)\)
An 8 ounce tube of toothpaste costs $1.69. What is the Unit Price per ounce?
Answers
Answer:
$0.21 per ounce (rounded to nearest cent)
Step-by-step explanation:
8 ounces --- $1.69
1 ounce --- \(\frac{1}{8}\) × $1.69 = $0.21 (rounded to nearest cent)
Question:
What is the Unit Price per ounce?
Answer:
If 8 ounces cost $1.69, then 1 ounce costs $1.69/8 = $0.21125, which is 21.125 cents, which rounds to 21.1 cents (because 2 is less than 5)
what is the nth term in a cube number sequence
Answers
Answer:
cube numbers: 1, 8, 27, 64, 125, ... - the nth term is. triangular numbers: 1, 3, 6, 10, 15, ... (these numbers can be represented as a triangle of dots).Step-by-step explanation:
IF IT HELPED UH PLEASE MARK ME A BRAINLIEST :-)Stephen was thinking of a number. Stephen doubles it, then adds 11 to get an answer of 47.7. What was the original number?
Answers
The original number in the statement is 18.5
How to determine the original number?The statements in the question are given as:
A number. Doubles the numberAdds 11 to the numberResult = 47.7Let the number be x
So, we have the following equation
2x + 11 = 47.7
Subtract 11 from both sides
2x = 36.7
Divide by 2
x = 18.35
Hence, the number is 18.35
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Find the value of X that makes m n
Answers
8
x = 6
9
x=7
10
x= 15
see explanation in image
because you know that m and n are parralell you can use the vertical angle theorem as well as the fact that lines in a straight angle add to 180
if you have any questions just comment
if 125% of a number is 750 what is 65% of the number
Answers
Answer:600
Step-by-step explanation:
We have, 125% * x = 750
Multiplying both sides by 100 and dividing both sides by 125
we have x = 750 * 100/125
you then get X=600
Answer:x=600
Step-by-step explanation: Multiplying both sides by 100 and dividing both sides by 125
Eva deposited these checks into her account $284.39, $15.44, $386.12. She received no cash back. What was her deposit total?
Answers
Hope it works, good luck!
A triangle has one side that measures 4 ft, one side that measures 6 ft, and one side that measures 9 ft.
What kind of triangle is it?
A. equilateral triangle
B. isosceles triangle
C. scalene triangle
D. right triangle
Answers
The given measures made up a scalene triangle. Therefore, option C is the correct answer.
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Given that, a triangle has one side that measures 4 ft, one side that measures 6 ft and one side that measures 9 ft.
A. All the sides are not equal, then it is not an equilateral triangle.
B. Any two sides are not equal, then it is not an isosceles triangle.
C. All the sides are equal, then it is a scalene triangle.
D. By using Pythagoras theorem,
9²=6²+4²
81≠52
So, the given measure does made up right triangle.
Therefore, option C is the correct answer.
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if you could help that would be greatly appreciated
Answers
Answer: search
Step-by-step explanation: look up the question on your browser and the answer will pop up
A puzzle has 1080 pieces. How many pieces are 80% of the puzzle?
Answers
Answer:
864
Step-by-step explanation:
80/100 simplified is 4/5
so you do 4/5 of 1080
which is 1080 divided by 5 that is 216
and then 216 x 4 which is 864
need a lil help please
Answers
Answer:
B(2, 4)Step-by-step explanation:
Given points:
A(-1, -9) and M(0.5, -2.5)Let the coordinates of B are (x, y)
Use midpoint formula to determine the point B:
0.5 = (- 1 + x)/2 ⇒ 1 = -1 + x ⇒ x = 1 + 1 = 2-2.5 = (-9 + y)/2 ⇒ -5 = -9 + y ⇒ y = -5 + 9 = 4Plsss helpp no links plss
Answers
Answer:
arrange them: -9x^3+2x^3-4x^2+x^2-6x-5x
the simplified is: -7x^3-3x^2-11x
geometry need help asap
Answers
The value of angle LAF in the intersecting chords is determined as 104⁰.
What is the value of angle LAF?The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
m∠LAF = ¹/₂ (arc LF + arc YS)
From the diagram, we have arc LF = 160⁰ and YS = 48⁰
m∠LAF = ¹/₂ (160 + 48)
m∠LAF = 104⁰
Thus, the value of angle LAF is calculated by applying intersecting chord theorem.
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Find f such that f'(x) = 8x – 3. f(4) = 0
Answers
Answer: y=29 / (4,29)
Step-by-step explanation:
By graphing \(f(x)=8x-3\) and \(f(4)=0\) on Desmos. You'll be able to find that when x is 4, y is 29.
Similarly, you can plugin 4 into the original equation (\(f(x)=8x-3\)) Which looks like:
\(8(4)-3\\32-3=29\)
Additionally, you can change \(f(x)=\) to \(y=\) as it is the exact same thing. With that in mind, you can do the same with \(f(x)=0\) and just change it to x=4. As you're wanting to know what the y-value is when x=4.
Answer:
4x²-3x+c is our original equation
Step-by-step explanation:
we have an independent number I called this number c
put 4 from x and try to find c
f(4)=4*(4²)-3*(4)+c=0
we have to be careful about f(4) is 0
64-12+c=0 and c is -52 so our original equation is 4x²-3x-52
Persent to a decinal 7%.
Answers
To express a percentage as decimal numbers you have to make the following convertion:
Consider that 100% is equal to 1, use cross multiplication to convert 7%:
100%____1
7%____x
\(x=\frac{7\cdot1}{100}=\frac{7}{100}=0.07\)So, remember, to transform any percentage in decimal numbers, just divide it by 100.